Three analytical problems in estimating the frequency at which commercial airline flights will encounter high cabin ozone levels are formulated and solved: namely, estimating flight-segment mean levels, estimating maximum-per-flight levels, and estimating the maximum average level over a specified flight interval. For each problem, solution procedures are given for different levels of input information - from complete cabin ozone data, which provides a direct solution, to limited ozone information, such as ambient ozone means and standard deviations, with which several assumptions are necessary to obtain the required estimates. Each procedure is illustrated by an example case calculation that uses simultaneous cabin and ambient ozone data obtained by the NASA Global Atmospheric Sampling Program. Critical assumptions are discussed and evaluated, and the several solutions for each problem are compared. Example calculations are also performed to illustrate how variations in lattitude, altitude, season, retention ratio, flight duration, and cabin ozone limits affect the estimated probabilities.